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# The letters "CFOSU" are arranged in dictionary order. What is the rank

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Math Expert
Joined: 02 Sep 2009
Posts: 64174
The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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11 Nov 2019, 00:49
10
00:00

Difficulty:

55% (hard)

Question Stats:

61% (01:48) correct 39% (01:38) wrong based on 85 sessions

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The letters "CFOSU" are arranged in dictionary order. What is the rank of the word "FOCUS" in this order?

(A) 17
(B) 21
(C) 31
(D) 32
(E) 38

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Joined: 18 Aug 2017
Posts: 6272
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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11 Nov 2019, 01:30
Bunuel wrote:
The letters "CFOSU" are arranged in dictionary order. What is the rank of the word "FOCUS" in this order?

(A) 17
(B) 21
(C) 31
(D) 32
(E) 38

Are You Up For the Challenge: 700 Level Questions

CFOSU = 4! ways
FCOSU = 3! ways
FOCSU = 1 and FOCUS ; 1
total 4!+3!+1+1 ; 32
IMO D
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Joined: 16 Dec 2019
Posts: 17
Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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11 Jan 2020, 10:45
Bunuel wrote:
The letters "CFOSU" are arranged in dictionary order. What is the rank of the word "FOCUS" in this order?

(A) 17
(B) 21
(C) 31
(D) 32
(E) 38

Are You Up For the Challenge: 700 Level Questions

Can somebody explain how to approach these questions

Thanks
Intern
Joined: 08 Jan 2020
Posts: 5
Location: Austria
Schools: HSG SIM "22 (A)
GMAT 1: 740 Q48 V44
GPA: 4
Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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25 Jan 2020, 01:12
It would be highly appreciated if someone could elaborate a little bit on this. Thanks
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3367
Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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25 Jan 2020, 08:43
1
1

Solution

Given
In this question, we are given that
• All the letters of “CFOSU” are arranged in dictionary order

To find
We need to determine
• The rank of the word “FOCUS”

Approach and Working out
If all the letters are arranged in alphabetical order, then we will have words starting with C first, then F, then O, then S, and finally U.

If C is the first word, then the remaining words can arrange themselves in 4! = 24 ways

Next, we will have words starting with F.
• Words starting with FC = 3! = 6
• Words starting with FOC: FOCSU and FOCUS

Hence, the rank of the word FOCUS = 24 + 6 + 1 + 1 = 32

Thus, option D is the correct answer.

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Joined: 10 Dec 2019
Posts: 52
Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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01 Feb 2020, 07:02
Can anyone recommend more faster or alternative approach here please?
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Joined: 03 Jun 2019
Posts: 2897
Location: India
GMAT 1: 690 Q50 V34
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Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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01 Feb 2020, 07:21
Bunuel wrote:
The letters "CFOSU" are arranged in dictionary order. What is the rank of the word "FOCUS" in this order?

(A) 17
(B) 21
(C) 31
(D) 32
(E) 38

Are You Up For the Challenge: 700 Level Questions

Words starting with letter C = 4! = 24
With F as first letter, words starting with C as second letter = 3! = 6
Words with F as first and C as second letter, O as third letter, S as fourth and U as fifth letter = 1
Ranking of word FOCUS = 24 + 6 + 1 + 1 = 32

IMO D
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Intern
Joined: 14 Jul 2019
Posts: 34
The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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01 Mar 2020, 01:02
Bunuel wrote:
The letters "CFOSU" are arranged in dictionary order. What is the rank of the word "FOCUS" in this order?

(A) 17
(B) 21
(C) 31
(D) 32
(E) 38

The first word in this order will be CFSOU

With C as starting letters, we have 4! ways = 24 arrangement.
With F as starting letters, we have FSxxx before FOxxx, so 3! = 6 more numbers before FOCUS.
With FO as starting letters, clearly C is the next one to go. So we have FOCxx.

Since U is behind S in the alphabet, we have FOCSU and then FOCUS. The rank of FOCUS is 24+6+1+1 = 32.
IMO D.

I hate this type of question so much. Singing the alphabet song to solve this kind of problems takes a huge toll on my manhood.
The letters "CFOSU" are arranged in dictionary order. What is the rank   [#permalink] 01 Mar 2020, 01:02